Question

Eight identical small solid spheres, each of
moment of inertia I' are recast to form a big
solid sphere. M.I. of the big solid sphere is
MH CET 2009)
(A ) 8 I
(B) 16 I
(C) 24 I
(D) 321​

Answer 1

Answer:

(a)

Explanation:

Answer 2

The moment of inertia of big solid sphere  is 32 I.

(D) is correct option

Explanation:

Given that,

Eight identical small solid spheres, each of  moment of inertia I'.

The moment of inertia of sphere is

$I=\dfrac{2}{5}mr^2$

Let the mass and radius of small solid sphere m and r

Mass of big solid sphere is 8m.

We need to calculate the radius of solid sphere is

Using formula of volume

Volume of eight small sphere = Volume of big sphere

$\dfrac{4}{3}\p\times (8r)^3=\dfrac{4}{3}\times\pi\times (R)^3$

$2r=R$

We need to calculate the moment of inertia of big solid sphere

Using formula of moment of inertia of sphere

$I'=\dfrac{2}{5}MR^2$

Put the value into the formula

$I'=\dfrac{2}{5}\times(8m)\times(2r)^2$

$I'=32\times\dfrac{2}{5}mr^2$

$I'=32\times I$

Hence, The moment of inertia of big solid sphere  is 32 I.

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Topic : moment of inertia

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